Level 29 • 19/50 questions • 35 seconds per question.
Login to save your score, XP, coins and progress.
What is the discriminant (D) of \(9x^2-12x+4=0\)?
A. (0)
यहाँ (D=(-12)2-4\cdot9\cdot4=144-144=0) है। (b) ऋणात्मक हो तो भी \(b^2\) धनात्मक होता है। / Here (D=(-12)2-4\cdot9\cdot4=144-144=0). Even if (b) is negative, \(b^2\) is positive.
Login to save your score, XP, coins and progress.
If (D=49), what will be the nature of roots of the quadratic equation?
A. दो भिन्न वास्तविक मूलTwo distinct real roots
(D=49>0), इसलिए दो भिन्न वास्तविक मूल मिलते हैं। विवेचक का चिन्ह मूलों की प्रकृति बताता है। / Since (D=49>0), two distinct real roots are obtained. The sign of the discriminant tells the nature of roots.
Login to save your score, XP, coins and progress.
What is the nature of roots of \(x^2-10x+25=0\)?
B. दो समान वास्तविक मूलTwo equal real roots
यहाँ (D=(-10)2-4\cdot1\cdot25=0), इसलिए मूल समान हैं। (D=0) समान वास्तविक मूलों की पहचान है। / Here (D=(-10)2-4\cdot1\cdot25=0), so the roots are equal. (D=0) identifies equal real roots.
Login to save your score, XP, coins and progress.
Which option has roots (x=2) and (x=7)?
A. \(x^2-9x+14=0\)
मूल (2) और (7) हों तो गुणनखंड ((x-2)) और ((x-7)) होंगे। इनका गुणन \(x^2-9x+14=0\) देता है। / If the roots are (2) and (7), the factors are ((x-2)) and ((x-7)). Their product gives \(x^2-9x+14=0\).
Login to save your score, XP, coins and progress.
If the roots are (-4) and (3), what will be the monic quadratic equation?
A. \(x^2+x-12=0\)
गुणनखंड ((x+4)) और ((x-3)) होंगे। इनसे \(x^2+x-12=0\) मिलता है। / The factors will be ((x+4)) and ((x-3)). These give \(x^2+x-12=0\).
Login to save your score, XP, coins and progress.
What are the roots of \(x^2+9x=0\)?
A. (0,-9)
(x-2+9x=x(x+9)), इसलिए मूल (0) और (-9) हैं। समान गुणनखंड निकालना जल्दी तरीका है। / (x-2+9x=x(x+9)), so the roots are (0) and (-9). Taking the common factor is a quick method.
Login to save your score, XP, coins and progress.
What are the roots of \(16x^2-81=0\)?
A. \(x=\pm \frac{9}{4}\)
\(16x^2=81\), इसलिए \(x^2=\frac{81}{16}\) और \(x=\pm\frac{9}{4}\) है। वर्गमूल लेते समय दोनों चिन्ह लें। / \(16x^2=81\), so \(x^2=\frac{81}{16}\) and \(x=\pm\frac{9}{4}\). Take both signs while taking square roots.
Login to save your score, XP, coins and progress.
If (x=-5) and (x=2) are roots, what is the sum of the roots?
A. (-3)
मूलों का योग (-5+2=-3) है। विपरीत चिन्ह वाली संख्याओं में बड़े परिमाण का चिन्ह आता है। / The sum of roots is (-5+2=-3). For numbers with opposite signs, the sign of the larger magnitude is used.
Login to save your score, XP, coins and progress.
If the roots are (-3) and (-8), what is the product of the roots?
A. (24)
मूलों का गुणनफल ((-3)(-8)=24) है। दो ऋणात्मक संख्याओं का गुणनफल धनात्मक होता है। / The product of roots is ((-3)(-8)=24). The product of two negative numbers is positive.
Login to save your score, XP, coins and progress.
Which quadratic equation has sum of roots (-6) and product (8)?
A. \(x^2+6x+8=0\)
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) होता है। योग (-6) रखने पर \(x^2+6x+8=0\) मिलता है। \(/ A monic equation is (x^2-(\)sum)x+product\(=0). Substituting sum (-6) gives (x^2+6x+8=0).\)
Login to save your score, XP, coins and progress.
What is the sum of roots of \(4x^2-7x+2=0\)?
A. \(\frac{7}{4}\)
मूलों का योग \(-\frac{b}{a}=-\frac{-7}{4}=\frac{7}{4}\) है। सूत्र में (b) का चिन्ह ध्यान से रखें। / The sum of roots is \(-\frac{b}{a}=-\frac{-7}{4}=\frac{7}{4}\). Pay attention to the sign of (b) in the formula.
Login to save your score, XP, coins and progress.
What is the product of roots of \(5x^2-3x-11=0\)?
A. \(-\frac{11}{5}\)
मूलों का गुणनफल \(\frac{c}{a}=\frac{-11}{5}\) है। (c) का चिन्ह सूत्र में सीधे आता है। / The product of roots is \(\frac{c}{a}=\frac{-11}{5}\). The sign of (c) is used directly in the formula.
Login to save your score, XP, coins and progress.
If the sum of roots of \(3x^2+nx+12=0\) is (-4), what is (n)?
A. (12)
मूलों का योग \(-\frac{n}{3}=-4\), इसलिए (n=12) है। योग के सूत्र में ऋण चिन्ह न भूलें। / The sum of roots is \(-\frac{n}{3}=-4\), so (n=12). Do not forget the negative sign in the sum formula.
Login to save your score, XP, coins and progress.
If the product of roots of \(px^2+6x+9=0\) is (3), what is the value of (p)?
A. (3)
मूलों का गुणनफल \(\frac{9}{p}=3\), इसलिए (p=3) है। गुणनफल के लिए \(\frac{c}{a}\) का प्रयोग करें। / The product of roots is \(\frac{9}{p}=3\), so (p=3). Use \(\frac{c}{a}\) for the product of roots.
Login to save your score, XP, coins and progress.
Which pair is the correct roots of \(x^2+2x-35=0\)?
A. (5,-7)
((x+7)(x-5)=0) से मूल (-7) और (5) मिलते हैं। गुणनफल और योग दोनों मिलाकर जांचें। / From ((x+7)(x-5)=0), the roots are (-7) and (5). Check both product and sum.
Login to save your score, XP, coins and progress.
If the roots of \(x^2+rx+36=0\) are (6) and (6), what is the value of (r)?
B. (-12)
मूलों का योग (12) है और \(x^2+rx+36=0\) में योग (-r) होता है। इसलिए (r=-12) है। / The sum of roots is (12), and in \(x^2+rx+36=0\) the sum is (-r). Therefore (r=-12).
Login to save your score, XP, coins and progress.
If the roots of \(x^2-14x+k=0\) are equal, what is (k)?
B. (49)
समान मूलों के लिए (D=0), इसलिए (196-4k=0) और (k=49)। समान मूल की शर्त में विवेचक शून्य रखें। / For equal roots, (D=0), so (196-4k=0) and (k=49). For equal roots, set the discriminant to zero.
Login to save your score, XP, coins and progress.
In \(x^2+kx+49=0\), if the roots are equal and positive, which possible value of (k) is correct?
B. (-14)
समान मूलों के लिए \(k^2=196\) और समान मूल \(-\frac{k}{2}\) होगा। धनात्मक मूल के लिए (k=-14) सही है। / For equal roots, \(k^2=196\), and the equal root is \(-\frac{k}{2}\). For a positive root, (k=-14) is correct.
Login to save your score, XP, coins and progress.
If the roots of \(x^2+sx+18=0\) are (-3) and (-6), what is the value of (s)?
A. (9)
मूलों का योग (-9) है और \(x^2+sx+18=0\) में योग (-s) होता है। इसलिए (s=9) है। / The sum of roots is (-9), and in \(x^2+sx+18=0\) the sum is (-s). Therefore (s=9).
Login to save your score, XP, coins and progress.
This level is designed for 50 active questions. Currently 19 questions are available for the selected class and difficulty.
Yes, the timer uses 35 seconds per question for Medium difficulty and shows the total remaining time on the page.
Yes, every question has its own SEO-friendly page with answer, explanation and related practice links.
Use Google login or mobile OTP. Admin can block users and control login providers.